A new approach to velocity averaging lemmas in Besov spaces

Diogo Arsénio; Nader Masmoudi

doi:10.1016/j.matpur.2013.06.012

A new approach to velocity averaging lemmas in Besov spaces

Research output: Contribution to journal › Article › peer-review

Abstract

We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.

Original language	English (US)
Pages (from-to)	495-551
Number of pages	57
Journal	Journal des Mathematiques Pures et Appliquees
Volume	101
Issue number	4
DOIs	https://doi.org/10.1016/j.matpur.2013.06.012
State	Published - Apr 2014

Keywords

Besov spaces
Dispersion
Kinetic transport equation
Velocity averaging

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1016/j.matpur.2013.06.012

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AB - We develop a new approach to velocity averaging lemmas based on the dispersive properties of the kinetic transport operator. This method yields unprecedented sharp results in critical Besov spaces, which display, in some cases, a gain of one full derivative. Moreover, the study of dispersion allows to treat the case of LxrLvp integrability with r ≤ p. We also establish results on the control of concentrations in the degenerate Lx,v1 case, which is fundamental in the study of hydrodynamic limits of the Boltzmann equation.

KW - Besov spaces

KW - Dispersion

KW - Kinetic transport equation

KW - Velocity averaging

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A new approach to velocity averaging lemmas in Besov spaces

Abstract

Keywords

ASJC Scopus subject areas

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